Joins and intersections:
Saved in:
| Main Authors: | , , |
|---|---|
| Format: | Book |
| Language: | German |
| Published: |
Berlin [u.a.]
Springer
1999
|
| Series: | Springer Monographs in mathematics
|
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | VI, 307 S. |
| ISBN: | 3540663193 |
Staff View
MARC
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Record in the Search Index
| _version_ | 1804127380224081920 |
|---|---|
| adam_text | Table of Contents
Introduction 1
Notations 5
1. The Classical Bezout Theorem 7
1.1 Degrees of Projective Schemes 7
1.2 Multiplicities of Local Rings 12
1.3 Joins 24
1.4 The Classical Bezout Theorem 32
1.5 Generic Bertini Theorems 36
2. The Intersection Algorithm and Applications 43
2.1 The Intersection Algorithm 44
2.2 Application I: The Refined Bezout Theorem 53
2.3 Segre Classes, v Cycles and Positivity 60
2.4 Segre Classes: The General Case 66
2.5 Limits of Joins and Intersections 74
3. Connectedness and Bertini Theorems 83
3.1 Connectedness Theorems 84
3.2 Applications to Intersections and Singularities of Mappings .. 91
3.3 Open Loci Results and the Generic Principle 98
3.4 Bertini Theorems 107
3.5 Grothendieck s Finiteness Theorem and Applications 113
3.6 A Relative Version of Krull s Principal Ideal Theorem 118
4. Joins and Intersections 123
4.1 Linear Projections 124
4.2 Tangencies of Algebraic Varieties 131
4.3 Embedded Tangent Spaces and Tangent Cones 136
4.4 Dual Varieties and the Gauss Map 142
4.5 Superadditivity of Join Defects 150
4.6 Joins, Vertices and Higher Join Varieties 157
4.7 Higher Secant Varieties of Rational Normal Scrolls 164
VI Table of Contents
5. Converse to Bezout s Theorem 171
5.1 Joins of Minimal Dimension 172
5.2 A Numerical Criterion for Proper Intersection 176
5.3 The Arithmetically Cohen Macaulay Case 183
5.4 A Local Version of Bezout s Theorem 186
6. Intersection Numbers and their Properties 193
6.1 A General Version of the j Multiplicity 193
6.2 Intersection Numbers 199
6.3 Criteria for Bounded Multiplicity 203
6.4 Examples and Problems 204
7. Linkage, Koszul Cohomology and Intersections 209
7.1 Linkage 209
7.2 Strongly Cohen Macaulay Subschemes 216
7.3 Linkage and the Strong Cohen Macaulay Property 225
7.4 Applications to Cones, Joins and Secant Varieties 232
7.5 Secant Varieties for Two Dimensional Singularities 239
7.6 Limits of Joins for Small Deviation 244
8. Further Applications 251
8.1 Generic Residual Intersections 252
8.2 Generic Projections and Double Point Cycles 255
8.3 Generic Projections and the Ramification Cycle 260
8.4 Trisecant Varieties and Inner Projections 268
A. Appendix 277
A.I Some Standard Results from Commutative Algebra 277
A.2 Gorenstein Rings 283
A.3 Historical Remarks 288
Bibliography 291
Index of Notations 299
Index 303
|
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| author | Flenner, Hubert 1951- O'Carroll, Liam Vogel, Wolfgang |
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| dewey-sort | 3516.3 15 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
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| id | DE-604.BV012716147 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-09T18:32:26Z |
| institution | BVB |
| isbn | 3540663193 |
| language | German |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-008644562 |
| oclc_num | 42291085 |
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| physical | VI, 307 S. |
| publishDate | 1999 |
| publishDateSearch | 1999 |
| publishDateSort | 1999 |
| publisher | Springer |
| record_format | marc |
| series2 | Springer Monographs in mathematics |
| spelling | Flenner, Hubert 1951- Verfasser (DE-588)10852552X aut Joins and intersections H. Flenner ; L. O'Carroll ; W. Vogel Berlin [u.a.] Springer 1999 VI, 307 S. txt rdacontent n rdamedia nc rdacarrier Springer Monographs in mathematics Algèbre commutative Algèbres commutatives ram Doorsneden (verzamelingen) gtt Géométrie algébrique Géométrie algébrique ram Intersections, Théorie des Intersections, Théorie des ram Verzamelingen (wiskunde) gtt Commutative algebra Geometry, Algebraic Intersection theory Schnitttheorie (DE-588)4179890-9 gnd rswk-swf Algebraische Geometrie (DE-588)4001161-6 gnd rswk-swf Algebraische Geometrie (DE-588)4001161-6 s DE-604 Schnitttheorie (DE-588)4179890-9 s O'Carroll, Liam Verfasser aut Vogel, Wolfgang Verfasser aut HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=008644562&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Flenner, Hubert 1951- O'Carroll, Liam Vogel, Wolfgang Joins and intersections Algèbre commutative Algèbres commutatives ram Doorsneden (verzamelingen) gtt Géométrie algébrique Géométrie algébrique ram Intersections, Théorie des Intersections, Théorie des ram Verzamelingen (wiskunde) gtt Commutative algebra Geometry, Algebraic Intersection theory Schnitttheorie (DE-588)4179890-9 gnd Algebraische Geometrie (DE-588)4001161-6 gnd |
| subject_GND | (DE-588)4179890-9 (DE-588)4001161-6 |
| title | Joins and intersections |
| title_auth | Joins and intersections |
| title_exact_search | Joins and intersections |
| title_full | Joins and intersections H. Flenner ; L. O'Carroll ; W. Vogel |
| title_fullStr | Joins and intersections H. Flenner ; L. O'Carroll ; W. Vogel |
| title_full_unstemmed | Joins and intersections H. Flenner ; L. O'Carroll ; W. Vogel |
| title_short | Joins and intersections |
| title_sort | joins and intersections |
| topic | Algèbre commutative Algèbres commutatives ram Doorsneden (verzamelingen) gtt Géométrie algébrique Géométrie algébrique ram Intersections, Théorie des Intersections, Théorie des ram Verzamelingen (wiskunde) gtt Commutative algebra Geometry, Algebraic Intersection theory Schnitttheorie (DE-588)4179890-9 gnd Algebraische Geometrie (DE-588)4001161-6 gnd |
| topic_facet | Algèbre commutative Algèbres commutatives Doorsneden (verzamelingen) Géométrie algébrique Intersections, Théorie des Verzamelingen (wiskunde) Commutative algebra Geometry, Algebraic Intersection theory Schnitttheorie Algebraische Geometrie |
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